Topic: intrinsic dimension

Optimal transport supports clustering, dictionary learning and domain adaptation, but high-dimensional data often force projections that discard information. Charles Bouveyron develops an alternative for Gaussian distributions with parsimonious covariance structure and low intrinsic dimension. A low-dimensional decomposition of empirical covariance matrices gives an efficient, robust closed form for the 2-Wasserstein distance without projecting the data. An explicit Monge map uses exact covariance square roots and inverse square roots. Numerical comparisons demonstrate analytical and computati

Artificial recurrent neural networks (RNNs) have become a customary research tool in theoretical neuroscience, being used as models of biological neural networks performing cognitive tasks. While RNNs are not generally intended as faithful, biologically realistic models of neuronal activity, there is a broad expectation that RNN dynamics may provide good models at the level of neural population dynamics. According to several authors, in both cases population activity should organize into low-dimensional manifolds encoding the relevant task variables (1). However, strong tests of this hypothesi